Uniform Dimension Results for the Brownian Sheet

A Uniform Dimension Resultfor the Brownian Snake 1

Small ball estimates for Brownian motion and the Brownian sheet

Small ball estimates for Brownian motion and the Brownian sheet are obtained when the balls are given by certain H61der norms. As an application, we establish some lira inf results for Gaussian samples of these processes, as well as Chung's LIL in this setting, but now we introduce some notation. Let I = [0, 1 ], with Co(I) the continuous real-valued function f ( . ) on I such that f ( 0 ) = 0....

Some polar sets for the brownian sheet

© Springer-Verlag, Berlin Heidelberg New York, 1997, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...

Slices of Brownian Sheet: New Results, and Open Problems

We can view Brownian sheet as a sequence of interacting Brownian motions or slices. Here we present a number of results about the slices of the sheet. A common feature of our results is that they exhibit phase transition. In addition, a number of open problems are presented. Mathematics Subject Classification (2000). 60G60, 60H99.

Images of the Brownian Sheet

An N-parameter Brownian sheet in Rd maps a non-random compact set F in R+ to the random compact set B(F ) in R d. We prove two results on the image-set B(F ): (1) It has positive d-dimensional Lebesgue measure if and only if F has positive d 2 -dimensional capacity. This generalizes greatly the earlier works of J. Hawkes (1977), J.-P. Kahane (1985), and Khoshnevisan (1999). (2) If dimH F > d 2 ...